How can I calculate the SD from the SE of a least square mean?

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I am conducting a meta-analysis and I need to collect mean and standard deviations (SDs). In some studies the raw means are not available and least square means are provided instead. Is there a way to calculate the SD from the Std.Err.?

Can we approximate the SD as $\text{SD} = \text{SE} \cdot \sqrt{N}$ as we would do for the mean?